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The derivation of the Helmholtz theorem of vector decomposition of a 3-vectorfield requires that the field satisfy certain convergence properties at spatialinfinity. This paper investigates if time-dependent electromagnetic radiationwave fields, which are of long range, satisfy these requirements. It is foundthat the requirements are satisfied because the fields give rise to integralsover the radial distance r of integrands of the form sin(kr)/r and cos(kr)/r.These Dirichlet integrals converge at infinity as required.

Does the Helmholtz theorem of vector decomposition apply to the wave fields of electromagnetic radiation?